Anatomy of Fishes:
            <i>Handbuch der Binnenfischerei Mitteleuropas</i>
            . H. H. Wunsch, Ed. vol. 2A,
            <i>Anatomie der Fische</i>
            . Wilhelm Harder. Schweizerbart'sche, Berlin, 1964. Text volume, xiv + 308 pp.; plates, vi + 115 pp. Illus. Paper, DM. 94; cloth, DM. 103.

Dyson, James L.

doi:10.1126/science.147.3660.852-a

Science

1965

DOI: 10.1126/science.147.3660.852-a

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Anatomy of Fishes: Handbuch der Binnenfischerei Mitteleuropas . H. H. Wunsch, Ed. vol. 2A, Anatomie der Fische . Wilhelm Harder. Schweizerbart'sche, Berlin, 1964. Text volume, xiv + 308 pp.; plates, vi + 115 pp. Illus. Paper, DM. 94; cloth, DM. 103.

James L. Dyson¹

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1980

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“…This is just the Lagrangian postulated by Gursey and Radicati, which gave rise to SU(6) as its static symmetry (24). There is no U(1) problem!…”

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Geometrical gauge theory of ghost and Goldstone fields and of ghost symmetries

Ne’eman

Thierry‐Mieg

1980

Proc. Natl. Acad. Sci. U.S.A.

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We provide a geometrical identification of the ghost fields, essential to the renormalization procedure in the non-Abelian (Yang-Mills) case. These are some of the local components of a connection on a principal bundle. They multiply the differentials of coordinates spanning directions orthogonal to those of a given section, whereas the Yang-Mills potential multiplies the coordinates in the section itself. In the case of a supergroup, the ghosts become commutative for the odd directions, and represent Nambu-Goldstone fields. We apply the results to chiral "flavor" SU(3)j X SU(3)iR and to SU(2/1). The latter reproduces a highly constrained Weinberg-Salam model.It has been known since 1963 (1) that a principal fiber bundle provides a precise geometrical representation of Yang-Mills gauge theories. After 1975 (2), this correspondence has been extensively applied to the study of self-dual solutions of the Yang-Mills equation (monopoles, instantons) and of global properties of the bundle, etc.We present here an entirely different domain of applications. First, we reproduce the recently suggested (3-5) identification of the Feynman-DeWitt-Faddeev-Popov ghost fields (6) essential to the renormalization procedure in the non-Abelian case, with local geometrical objects in the principal bundle. This will directly yield the Becchi-Rouet-Stora (BRS) equations (7) guaranteeing unitarity and Slavnov-Taylor invariance (8, 9) of the quantum effective Lagrangian. Except for the "antighost" variation, this quantum-motivated symmetry thus corresponds to "classical" (geometrical) notions, with its dependence on the gauge-fixing procedure (which determines the quantized Lagrangian) limited to section dependence, a mere choice of gauge.We then consider the case of a supergroup (10) as an internal symmetry gauge, generalizing the recently suggested (11) role of SU(2/1). We show how the ghosts geometrically associated to odd generators (12) may be identified with the GoldstoneNambu (13) scalar fields of conventional models with spontaneous symmetry breakdown. As an example, we realize the chiral SU(3)L X SU(3)R "flavor" symmetry (14-16) by gauging the supergroup Q(3) (see refs. 10 and 12).Lastly, we recall some of the more relevant results concerning asthenodynamics (weak electromagnetic unification) as given (11) by the ghost-gauge SU(2/1) supergroup.Connections on a principal bundle: Gauge (potentials) and ghost fields We start by reintroducing (17, 18) the concept of a connection on a principal fiber bundle (P,M,7rG,-). Previous the Wa were identified with the Yang-Mills potentials. In our treatment, the connection w has m + n dimensions holonomically, Coa (R = ,u, i; ,u = 0,. .. 3; i = 1, ... n), quite aside from the n components described by the a index and contracted with the abstract Lie algebra matrices Xa. We denote the (vertical) projection by 7r:P o M, the structure group by G, and right-multiplication on P by the dot (-):P X G -P, sothatand for U., a neighborhood of x E M, we get "local triviality"(a direct prod...

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“…This is just the Lagrangian postulated by Gursey and Radicati, which gave rise to SU(6) as its static symmetry (24). There is no U(1) problem!…”

mentioning

confidence: 99%

“…[24] The t are in fact parameters of the axial generators. We denote the more common parameter of the (linear) vector subgroup by a.…”

mentioning

confidence: 99%

Geometrical gauge theory of ghost and Goldstone fields and of ghost symmetries

Ne’eman

Thierry‐Mieg

1980

Proc. Natl. Acad. Sci. U.S.A.

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show abstract

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Anatomy of Fishes: Handbuch der Binnenfischerei Mitteleuropas . H. H. Wunsch, Ed. vol. 2A, Anatomie der Fische . Wilhelm Harder. Schweizerbart'sche, Berlin, 1964. Text volume, xiv + 308 pp.; plates, vi + 115 pp. Illus. Paper, DM. 94; cloth, DM. 103.

Cited by 1 publication

References 0 publications

Geometrical gauge theory of ghost and Goldstone fields and of ghost symmetries

Geometrical gauge theory of ghost and Goldstone fields and of ghost symmetries

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